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IOSR Journal of Applied Physics (IOSR-JAP)
e-ISSN: 2278-4861.Volume 7, Issue 4 Ver. I (Jul. - Aug. 2015), PP 17-25
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N-Channel Silicon MOSFET As A Device To Characterize MIS
Structures By The BOEMDET Technique
Ravi Kumar Chanana
Department of Electrical and Electronics Engineering, Galgotia’s College of Engineering and Technology,
Affiliated to Uttar Pradesh Technical University, Lucknow,
1, Institutional Area, Knowledge Park-II, Greater Noida – 201306, Gautam Budh Nagar, U.P., India.
Abstract: Metal-Insulator-Semiconductor (MIS) characterization is performed utilizing two n-channel Si
MOSFET devices that provide both the electron tunneling current and the substrate hole current. The
characterization results in parabolic electron and hole effective mass values in thermal SiO2 of 0.42m and
0.58m respectively, the bandgap of SiO2 of 8.9 eV and the conduction and valence band offsets of 3.2 eV and 4.6
eV. The characterization technique called BOEMDET is suited for insulators with or without bulk traps and
exhibiting only Fowler-Nordheim (FN) type conduction at high electric fields. Also, the 1/E model of the anode
hole injection over the hole barrier of 4.6 eV completely explains the oxide breakdown in thin oxides of 5 to
10nm at high electric fields, and having a slope constant of about 505-509 MV/cm.
Keywords: effective mass, FN-tunneling, band offsets, metal-insulator-semiconductor
I. Introduction
In this report, gate tunneling electron current and substrate hole current versus gate voltage
characteristics of two n+ polysilicon gated n-channel MOSFETs are analyzed to characterize the metal-oxidesemiconductor device structure. The MOSFET data were reported by Eitan and Kolodny in 1983 and Rasras et
al. in 2001. The first device has a thermal oxide of 8.5 nm and a substrate bias of -1V [1]. The second device
has a thermal oxide of 7.7nm and the substrate is grounded [2]. The analysis on the device data provide the
electron and hole effective masses in the thermal silicon dioxide, the conduction and valence band offsets to the
oxide band edges, and the bandgap of the SiO2. This MIS characterization can be generalized to any dielectric
other than SiO2 that contains negligible bulk traps, so as to exhibit only Fowler-Nordheim type current-voltage
characteristics. Any significant amount of bulk traps will result in Poole-Frenkel type conduction. For a
dielectric containing bulk traps, photoemission techniques are suited for determining the band offsets and
bandgaps. These techniques do not interfere with the bulk traps [3, 4]. The dielectrics containing bulk traps
may also exhibit FN conduction at high electric fields greater than 8 MV/cm.
Next, the author reviews his previous research efforts in this area. In the year 2000, the confirmed
occurrence of Fowler-Nordheim hole tunneling in p-4H-SiC MOS device was reported [5]. The effective mass
of holes in the oxide was reported as 0.35m, which was less than the electron effective mass in SiO2 of 0.42m
[6]. The anode field correction was applied later to the current-voltage data giving the hole effective mass value
as 0.58m. This was reported in 2011 by the author [7]. In May-June 2014, the author characterized the MIS
structure utilizing a polysilicon gated silicon n-channel MOSFET [8]. The formulation and calculations in this
report required the threshold voltage for the MOSFET. An experimental value of 1.25 V was taken with the
MOSFET having a substrate bias of -1V. The hole effective mass in SiO2 obtained by this analysis was also
0.58m, as obtained earlier in p-4H-SiC MOS device [7]. In July-August 2014, the technique for MIS
characterization was proposed called BOEMDET which used only the electron and hole current slope constants
Be and Bh values to characterize the MIS structure [9]. In this technique, either a pair of MOS devices or an nchannel MOSFET were proposed to be utilized for the characterization. Subsequently, it was thought that the
MOSFET in inversion may have the same oxide voltage for both the electron and hole currents and this may
yield erroneous hole effective mass. Therefore, only one pair of silicon MOS devices, one n-type and one ptype was proposed to be the devices of choice for the BOEMDET technique. This proposal was reported in
November-December 2014, along with the applications of BOEMDET [10]. It is now clear that the voltage in
an oxide without charges for electron and hole conduction in a MOSFET are different and are formulated in the
present study.
Now, after renewed understanding, the MOSFET device in inversion is also thought to provide equally
good MIS characterization which could be accurate if the experimental threshold voltage is used in place of the
theoretical one [8, 9]. The Si n-channel MOSFET in inversion, under the new perspective is viewed as a
minority accumulated MOS device, when biased well in strong inversion with the electrons also supplied from
the source contact under bias. The source contact is either pulled down to the substrate bias of -1V [1] or,
grounded [2]. This article characterizes the MIS structure utilizing both the MOSFETs resulting in carrier mass
DOI: 10.9790/4861-07411725
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N-channel Silicon MOSFET as a device to characterize…
values in SiO2, band offsets and SiO2 bandgap values. To an accuracy of one decimal place for the band offsets
and bandgap of SiO2 and two decimal places for the carrier masses in SiO2, these values are same as reported
earlier [6-9]. It thus confirms the validity of the MOSFET model for MIS characterization. It incorporates new
result on the grounded MOSFET and a refined analysis of the voltage correction factor.
II.
Theory:
Fowler-Nordheim (FN) electron and hole tunneling has been observed in Si and SiC MOS devices and
in organic light emitting diodes [5-6, 11-12]. The FN equation models the current-voltage characteristics across
a MOS device at high fields. It is given by the classical equation [13]:
J
B
 A exp 
(1) ;
2
E
 E 
where J is the current density across the MOS device in A/cm 2, E is the oxide electric field in V/cm, and the preexponent A and the slope constant B are given by:
e3m
(2)
16 2 mox0
m 1
A  1.54 x10 6
( A / V 2 )
mox 0
A
4 2mox 
B
3
e
1/ 2
0 3 / 2 (3)
1/ 2
m 
3/ 2
B  6.83x10  ox  0 (V / cm)
 m 
7
In A and B constants, e is the electronic charge, m is the free electron mass, mox is the electron or hole mass in
the oxide, 2𝜋ℏ is Planck's constant and  0 is the electron or hole barrier height expressed in electron volts. A
plot of ln(J/E2) versus 1/E, called an FN plot, gives the value of the slope constant B, from which
mox / m1 / 2 0 3 / 2 product can be obtained.
Then, with a known effective mass,
0
can be calculated, and with
a known  0 , the effective mass in the oxide can be calculated. The slope constant B is very sensitive to the
oxide field as it is in the exponential and therefore precise determination of the oxide field is absolutely critical
in the evaluation of the tunneling parameters. The ln(J/E 2) term is relatively much less sensitive to the oxide
field as it is in the natural logarithm. The slope constant B can be independently used to determine the carrier
effective masses, band offsets at the insulator-semiconductor surface and the insulator bandgap, without the
knowledge of band offsets from photoemission spectroscopic measurements. This however is possible on the
silicon substrate, where the grown or deposited dielectric film forms an abrupt interface and the intrinsic Fermi
level of silicon lies very near the middle of its bandgap after the growth or deposition of the film due to
negligible intrinsic defects in the silicon substrate. The slope constants for electron current Be, and for the hole
current Bh, can be obtained from the current-voltage characteristics of an n-channel MOSFET. Fig. 1 presents a
n+ polysilicon gated n-channel MOSFET device in inversion with grounded substrate.
A. Oxide voltage formulation in a polysilicon gated n-channel MOSFET
An n-channel MOSFET device in inversion requires the threshold voltage VT as the positive charge on
the gate terminal of the MOSFET to basically invert the channel with electrons and thus form a parallel plate
capacitor with the gate as the anode and the channel as the cathode. This positive charge can be assumed to
reside at the gate separate from the applied voltage Vg across the capacitor. Now, if Vg is a voltage applied at
the gate anode, then this positive charge will enhance the field at the cathode for electron tunneling. So, in an
oxide without charges, the gate voltage should be reduced by V T, so that with charges the gate voltage is Vg-VT
+ VT equal to Vg which is same as in an ideal oxide. Thus the gate voltage for electron tunneling from the
cathode in an oxide without charges is Vg-VT. The positive charge VT reduces the field at the anode for hole
conduction, Thus in an oxide without charges, the gate voltage should be enhanced to Vg + VT, so that the gate
voltage with charges is equal to Vg+VT – VT equal to Vg, same as in an ideal oxide. Thus the gate voltage for
hole injection and conduction from the anode in an oxide without charges should be Vg +V T. The effect of the
charges is elaborated in the author’s earlier discussions [7, 10]. Based on the above explanation, the oxide
voltage for gate tunneling electron current and substrate hole current for an oxide without charges is formulated
next.
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N-channel Silicon MOSFET as a device to characterize…
Fig.1. Energy band diagram of a n-channel Si MOSFET device in inversion.
In an ideal MOS diode, if the applied voltage across the diode is V, then −𝑄𝑑 𝐶𝑖 is the voltage across
the oxide [14]. For an n-channel MOSFET Qd is negative, giving a positive voltage across the oxide insulator.
The threshold voltage for strong inversion, VT for a practical MOS device is expressed as:
𝑄
𝑄
𝑉𝑇 = 𝜑𝑚𝑠 − 𝐶 𝑖 − 𝐶𝑑 + 𝑉𝑠𝑖𝑛𝑣
(4)
𝑖
𝑖
where, 𝜑𝑚𝑠 is the metal-semiconductor work function difference, Qi is the oxide insulator charge density, Ci is
the oxide insulator capacitance per unit area, Qd is the depletion charge density in the semiconductor, and Vsinv is
twice the bulk potential in the semiconductor at which strong inversion occurs for the MOS device. For an
applied voltage VT across the MOS device, ideally -Qd/Ci will fall across the oxide. So, the voltage across the
oxide -Qd/Ci can be expressed as:
𝑉𝑜𝑥 = 𝑉𝑇 − 𝑉𝑓𝑏 − V𝑠𝑖𝑛𝑣
(5)
Where𝑉𝑓𝑏 = 𝜑𝑚𝑠 − 𝑄𝑖 𝐶𝑖 is the flatband voltage. Next, if the applied voltage is𝑉 − 𝑉𝑠𝑏 , then the expression
for the oxide voltage becomes:
Q
𝑉𝑜𝑥 = 𝑉 − 𝑉𝑠𝑏 − 𝑉𝑓𝑏 − V𝑠𝑖𝑛𝑣 − Vpoly + Cinv .
(6)
i
Here, 𝑉𝑠𝑏 is the reverse bias applied to the substrate of a MOSFET. It is used to control the threshold
voltage in a MOSFET, Vpoly is the polysilicon depletion potential that can increase to 0.97V equal to its
bandgap, when the MOSFET is biased well into strong inversion [15], and is more appropriately placed in the
expression for Vox instead of VT because polysilicon depletion increases at higher applied voltages. The value
of 0.97 V is derived from the fact that there is a 150meV band gap narrowing in 5 x 1019/cm3 doped Si [16], and
assuming that Si and polysilicon have the same band gap of 1.12 eV. Qinv/Ci is the potential drop in the electron
inversion layer in MOSFET. When the MOSFET is biased well into strong inversion, the centroid of the
inversion layer can be as much as 100nm, and the potential drop in the inversion layer can be calculated to be
lower than 0.05V [17]. This is small and can be ignored, although it brings a small uncertainty in the oxide
voltage formula. For an n+ polysillicon gated n-channel MOSFET biased well into inversion, the applied
voltage V between the gate anode and substrate cathode is positive, giving positive voltage drops V ox, Vsinv and
Vpoly. Vsb and Vfb are negative in the Vox expression and Qinv is negative due to electrons as the inversion
charge. Also, VT is positive and Qd is negative with Qd being modified due to the application of Vsb. From the
initial explanation for the gate voltage across the MOSFET for electron and hole conduction, the oxide voltage
for gate electron tunneling is given as above and the oxide voltage for hole injection and conduction from the
anode can be written as:
Q
𝑉𝑜𝑥 = 𝑉 − 𝑉𝑠𝑏 + 𝑉𝑓𝑏 + V𝑠𝑖𝑛𝑣 + Vpoly − Cinv .
(7)
i
From equation (4), (Vfb + Vsinv) is replaced by (VT + Qd/Ci). This is considered so that the experimental
threshold voltage value determined from the linear extrapolation technique of the ID-VGS curve at small VDS of
20 to 50 mV in the linear region of the MOSFET channel, can be utilized to find the oxide voltage for higher
accuracy. In a review article on threshold voltage determination techniques, eleven different techniques
including the above are discussed with six out of eleven techniques yielding the same threshold voltage in the
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N-channel Silicon MOSFET as a device to characterize…
studied long-channel MOSFET [18]. It has been shown in the author’s previous work, that the experimentally
determined VT by the above technique gives precise results of carrier masses [8, 9]. The above modification and
ignoring Qinv/Ci will change the equations (6) and (7) for the oxide voltage as below:
Q
𝑉𝑜𝑥 = 𝑉 − 𝑉𝑠𝑏 − 𝑉𝑇 − d − Vpoly .
(8)
Ci
𝑉𝑜𝑥 = 𝑉 − 𝑉𝑠𝑏 + VT +
Qd
Ci
+ Vpoly .
(9)
By considering Vpoly to be part of the threshold voltage equation (4), particularly for thin oxides of 5 to
10nm as in the author’s previous study [8, 9], the equations (8) and (9) reduce to the author’s previous
formulation [8, 9], keeping in view that the VT for a n+ polysilicon gated n-channel MOSFET is positive and Qd
is negative. Now, for a particular technology V sb may or may not be employed. Vfb depends mainly on the
metal-semiconductor work function difference in the silicon technology as Qi charge density is low. Vsinv
depends on the doping concentration of the p-well which is 1018/cm3 for the twin tub Si CMOS technology [19].
The Vpoly will exist only in case of polysilicon gates and will be absent for a metal gated MOSFET device. The
electron tunneling across the oxide is represented by the gate current in the n-channel MOSFET. The substrate
hole current in the n-channel MOSFET is believed to be due to the back injection of hot holes from the
polysilicon anode having the hole barrier of 4.6eV from the valence band of the polysilicon anode to the oxide
valence band [20]. Once the hot holes come into the valence band over the barrier, the hole current follows the
exp (-B/E) dependence of the FN tunneling equation (1) through the oxide.
B. Modification of the FN slope constant equations for devices on silicon
It has been observed from a recent report of Ultraviolet photoemission and Inverse photoemission
spectroscopic experiments on 2nm dry thermal SiO2 [4], that the conduction and valence band offsets from the
intrinsic silicon Fermi level are 3.8 eV and 5.1 eV respectively, and the bandgap of SiO 2 is 8.9 eV [4, 21].
Taking the ratios of these values as 3.8/8.9 and 5.1/8.9 gives the electron and hole effective masses in the SiO 2
of 0.427m and 0.573m respectively. Within the experimental error of ±0.1 eV in the measurements of band
offsets, the masses can be valued as 0.42m and 0.58m as reported earlier [7]. This ratio describes the ratio of the
photo-emitted electron or hole kinetic energies during photoemission into the oxide conduction and valence
bands as
0.5mox,e v 2
0.5(mox,e  mox,h )v 2
which equals
mox,e
m
, thus giving the ratio of electron effective mass to the
sum of electron and hole effective masses. Here, v is the drift velocity of the electron or hole in the oxide. The
sum of the electron and hole effective masses equals the free electron mass for the amorphous insulators and
therefore the band offsets to insulator bandgap ratio equals the relative carrier effective masses.
Thus, the relative electron and hole effective masses
h  0.57 
Eg
mox,e
m
and
mox,h
m
can be written as
e  0.55
when the insulator is grown or deposited on Si<100> or Si<111> surface. Here,
Eg
e
and
is the
electron band offset from silicon conduction band to oxide conduction band and  h is the hole band offset from
the silicon valence band to insulator valence band and 0.55 and 0.57 eV are added respectively to coincide the
band offsets from the intrinsic Fermi level of silicon. The intrinsic Fermi level E i of silicon is given by:
Ei 
Ec  Ev kT  N v 

ln   (10)
2
2  Nc 
where Ec is the bottom of the conduction band, Ev is the top of the valence band, Nc is the effective density of
states in the conduction band, and Nv is the effective density of states in the valence band. Nc for silicon equals
2.8 x 1019/cm3 and Nv equals 1.04 x 1019/cm3 at 300K temperature [22]. Evaluating the above equation gives the
position of intrinsic Fermi level of silicon about 0.01 eV above the middle of the silicon bandgap. Thus 0.55 eV
is added to  e and 0.57 eV is added to  h for the conduction and valence band offsets from the intrinsic Fermi
level of silicon. If Be and Bh are the electron and hole tunneling slope constants, then the slope constant
equations can be written as below:
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N-channel Silicon MOSFET as a device to characterize…
1/ 2
 mox,e
Be  6.83x10 
 m



 mox,h
Bh  6.83x10 
 m
mox,e



7
7
Substituting for
m
e 3 / 2 (11)
1/ 2
and
 h 3 / 2 (12)
mox,h
   0.55 

Be  6.83x10 7  e
 E

g


, the equations become
m
1/ 2
e 3 / 2 (13)
1/ 2
   0.57 
  h 3 / 2 (14)
Bh  6.83x10  h
 E

g


E g  e  h  1.12(15)
7
The equations (13), (14), and (15) form three non-linear simultaneous equations with three unknowns
that can be solved with a simple MATLAB software program or by trial and error for a given Be and Bh values.
This evaluation will result in the values of  e ,  h and Eg. Following this evaluation, the band offsets from
the intrinsic silicon Fermi level can be obtained. Further, the carrier effective masses and the unknown bandgap
of the insulator can be determined. This technique of characterizing an MIS structure is called BOEMDET by
the author [9, 10]. The character of an MIS structure can thus be described by the below mentioned Table as:
e
h
Eg
me
mh
C. Calculation of the corrected Slope constants B e and Bh
The corrected oxide voltages can be calculated as given in the above analysis. The slope constant B
given in equation (3) is determined from the I-V characteristics using equation (1). First 𝛥𝑙𝑛 𝐽 𝐸 2 𝛥 1 𝐸 is
calculated by taking at least two points on the I-V characteristics in the FN regime at high fields utilizing the
applied gate voltage. This yields the uncorrected B. Next, the corrected B is calculated by dividing 𝛥𝑙𝑛 𝐽 𝐸 2
by𝛥 1 𝐸 , with E obtained from the corrected oxide voltages corresponding to the same current density J as for
the uncorrected B.
III.
Results And Discussion
Two results are presented in this section. The first one highlights the difference between the
experimental VT obtained by finding the gate voltage axis intercept of the linear extrapolation of the ID-VGS
curve at the point of maximum transconductance of a MOSFET in the linear region [18], and the theoretical VT
obtained from equation (4) which is the same as the ID=0 point of the actual ID-VGS curve in the linear region.
Obviously, the experimental VT is larger than the theoretical VT. The second result is characterization of a MIS
structure giving the band offsets, carrier masses and band gap of the insulator which is thermal SiO2 in the
present study.
The experimental and theoretical threshold voltage is arrived at in rows (9) and (10) in Table I, after
determining the various parameters for a 50nm thick oxide from Fig.43 of reference [23]. It can be observed
that the experimental VT is obviously larger than the theoretical one based on their definitions. If the thickness
of the 50nm oxide is reduced to 8.5nm [1], then the voltage drop in the oxide given by
-Qd/Ci reduces to
0.19V from 1.09 V given in row (4). The experimental VT for the 50nm oxide with -1V substrate bias has been
determined as 1.25 V as given in Fig. 43 of reference [23]. Since Qd/Ci is -1.09 V for the same oxide, therefore
VT + Qd/Ci becomes 0.16 as given in row (12) of Table I. This is a typical value for all the technologies with
different substrate/channel doping and oxide thicknesses. Adding Vpoly of maximum 0.97 V to this value gives
the voltage correction factor to the oxide voltage equations (8) and (9) as 1.13 V. This is given in row (13) of
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N-channel Silicon MOSFET as a device to characterize…
Table I. This method for voltage correction has also been presented in an earlier study for electron conduction
in the oxide [15].
Table I. Various MOSFET parameters and their values obtained for 50nm and 8.5nm thick gate oxide to
provide the theoretical threshold voltage of the MOSFET.
S.No. Parameters
1.
2.
𝜓𝑠 = 2𝜓𝑏 = 2
𝑘𝑇
𝑁𝐴
𝑙𝑛
𝑞
𝑛𝑖
𝑄𝑑 = − 2𝑞𝜀𝑠 𝑁𝐴 𝜓𝑠 − 𝑉𝑠𝑏
50nm thick SiO2 [23]
8.5nm thick SiO2 [1]
0.7 V with NA=1016/cm3
0.7 V
and ni=1.45 x 1010/cm3
-7.55 x 10-8 Coul/cm2
-7.55 x 10-8 Coul/cm2
with εs=11.9ε0 and Vsb = -1V
3.
𝐶𝑖 =
𝜀0 𝜀𝑟
𝑑
6.9 x 10-8 F/cm2
40.6 x 10-8 F/cm2
4.
𝑄𝑑
𝐶𝑖
-1.09 V
-0.19 V
5.
𝜑𝑚𝑠 = −(0.55 + 𝜓𝑏 )
-0.898 V
-0.898 V
3.2 x 10-9 Coul/cm2
3.2 x 10-9 Coul/cm2
0.045 V
0.008 V
-0.944 V
-0.91 V
0.836 V
-0.02 V
1.25 V
0.35 V (expected)
-0.244 V
-0.21 V
+0.16 V
+0.16 V (expected)
1.13 V
1.13 V
6.
7.
8.
Qi = q.2 x 1010
𝑄𝑖
𝐶𝑖
𝑉𝑓𝑏 = 𝜑𝑚𝑠 −
𝑄𝑖
𝐶𝑖
9.
Theoretical 𝑉𝑇 = 𝑉𝑓𝑏 −
10.
Experimental 𝑉𝑇
11.
Theoretical 𝑉𝑇 +
12.
Experimental 𝑉𝑇 +
13.
Experimental VT 
𝑄𝑑
𝐶𝑖
+ 2𝜓𝑏
𝑄𝑑
𝐶𝑖
𝑄𝑑
𝐶𝑖
Qd
 V poly
Ci
The gate tunneling electron current and the substrate hole current versus the applied voltage characteristics of a
grounded n+ polysilicon gated n-channel MOSFET [2] shown in Fig.6 of reference [2] are taken as observations
(V1, I1), and (V2, I2) and presented in Table II. There could be small errors in reading the values from a
published article. Even a 0.1 V reading error has significant change in the calculated slope constant values. The
slope constants for the current versus oxide voltage data at high oxide fields are calculated next, as described in
the theory section followed by the calculations of band offsets, bandgap of SiO2, and the carrier effective masses
in the SiO2 by the BOEMDET technique [9, 10]. These observations and results are then tabulated below as
Table II and Table III. The corrected oxide voltages Vox11 and Vox22 in Table II are calculated using equations
(8) and (9) with the voltage correction factor given in row (13) of Table I as 1.13 V. The oxide voltages in
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N-channel Silicon MOSFET as a device to characterize…
Table II are accordingly corrected by 1.13 V followed by the calculation of the corrected slope constants Be and
Bh as given in Section C of the theory. With these Be and Bh values, equations (13), (14) and (15) are solved
simultaneously to give the data of Table III to represent the MIS structure. For an accuracy of one decimal
place the SiO2 bandgap value is 8.9 eV and CB and VB band offset values are 3.2 eV and 4.6 eV. The electron
and hole effective mass values are 0.42m and 0.58m to two decimal places.
Table II. Calculated slope constants from gate tunneling electron current and substrate hole current
versus oxide voltage characteristics at high oxide fields in a n+ polysilicon gated n-channel MOSFET
having 7.7nm thermal oxide and grounded substrate [2].
V1/Vox11
I1
V2/Vox22
I2
(V)
(A)
(V)
(A)
Slope constant
Be and Bh
(MV/cm)
8.0/6.87
10-8
10.0/8.87
10-5
254
8.4/9.53
10-11
11.0/12.13
10-7
505
Current Type
Gate tunneling
electron
current
Substrate hole
current over
anode barrier
Table III. Calculated band offsets, band gap of thermal oxide and carrier effective masses in SiO 2
Electron Band offset,
e
(eV)
Hole Band Offset
 h (eV)
3.205
SiO2 Bandgap
4.558
Eg
(eV)
Electron effective
mass
8.883
me in SiO2
Hole effective mass m h
in SiO2
0.422m
0.577m
The voltage correction factor of 1.13 V has also been applied to the I-V characteristics of a n-channel
MOSFET having -1V substrate bias [1, 8]. The MIS characterization for this device also resulted in similar
values as given in Table III for the grounded MOSFET to the same accuracy of one decimal place for the
bandgap and band offset values and two decimal places for the carrier effective mass values. This result is
presented in Table IV and V below. The earlier study [1, 8] had assumed a Vpoly of 0.9 V instead of the present
0.97 V as part of the threshold voltage of 1.25 V to give a correction factor of 1.06 V.
Table IV. Calculated slope constants from gate tunneling electron current and substrate hole current
versus oxide voltage characteristics at high oxide fields in a n+ polysilicon gated n-channel MOSFET
having 8.5nm thermal oxide and a substrate bias of -1V [1].
Current
V1/Vox11
I1
V2/Vox22
I2
(V)
(A)
(V)
(A)
8.0/7.87
10-8
9.45/9.32
10-6
253
9.47/11.60
10-9
11.0/13.13
10-7
509
Type
Gate tunneling
electron current
Substrate hole
current over anode
barrier
Slope constant Be
and Bh
(MV/cm)
Table V. Calculated band offsets, band gap of thermal oxide and carrier effective masses in SiO 2
Electron Band offset,
e
(eV)
Hole Band Offset
 h (eV)
3.201
4.581
SiO2 Bandgap
Eg
8.902
(eV)
Electron effective
mass
me in SiO2
0.421m
Hole effective mass
mh
in SiO2
0.579m
Two different types of samples are proposed by the author for the MIS characterization. One, a pair of
n-MOS and p-MOS Si devices in accumulation are used [10]. The second, an n-channel Si MOSFET device in
inversion that provides both the electron and hole current [8]. It is believed that for exact calculations, a pair of
MOS devices in accumulation should be preferred but it requires poly-silicon carbide gates [10]. The use of the
MOSFET device will become suitable with metal gated device to remove uncertainty in V poly.`
The origin of the substrate current in n-MOSFETs having thin oxide from 5 to 10nm is under debate [1,
2, 20, 24]. Eitan and Kolodny were one of the first to observe substrate hole current in n-channel MOSFET
having 8.5nm oxide, and attributed the hole current to the valence electron tunneling from the Si substrate
having a barrier of 4.3eV from the Si valence band to the oxide conduction band [1]. DiMaria et al. proposed
later that these holes originate as hot holes from the polysilicon anode. The energy for the hot holes are provided
by the FN tunneling electrons from the cathode, which have a threshold average energy of about 5eV from the
DOI: 10.9790/4861-07411725
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N-channel Silicon MOSFET as a device to characterize…
bottom of the oxide conduction band. These hot holes are concluded to be back injected from the anode over
the hole barrier at the Si anode for thin oxides of 5 to 10nm. In these thin oxides, the electron transport is quasiballistic, so that the maximum electron energy at the anode is independent of the oxide thickness giving a
thickness independent threshold [20]. More recently, the substrate holes are experimentally shown to be
generated by FN-induced photons in the polysilicon gate [2]. A report after the above, refuted this process of
hole generation and concluded that the generation efficiency of photons with energy above the Si bandgap
energy is 10-4 times smaller than that of the electron-hole pairs by impact ionization [24]. The above studies,
leads the author to believe that the hot holes from the anode are back injected into the oxide over the barrier [20,
25]. After coming to the oxide valence band, the hole current follows the exp (-B/E) dependence of the FN
tunneling equation (1). The calculated hole effective mass based on this dependence is exactly the same as that
determined from the FN tunneling of holes observed in p-4H-SiC MOS devices in accumulation [7]. This value
of hole effective mass is 0.58m for a free Fermi gas model of carriers at the emitting electrode. A value of
0.57m has been used earlier as a fitting parameter in a high frequency tunnel emitter transistor model [26]. The
value is also consistent with the evidence of light holes near the top of the oxide valence band [27].
The oxide breakdown in thin oxide films of 5 to 10nm is intimately related to the substrate current due
to hot holes, which is proportional to exp (-B/E) at high electric fields with the slope constant B of about 505509 MV/cm presented in Table II and IV. An n-channel silicon MOSFET when biased in inversion as shown in
Fig. 1 results in FN tunneling of electrons from the cathode into the oxide due to the smaller electron barrier to
oxide conduction band of 3.2 eV. They then arrive at the polysilicon anode, where they impact ionize and
create hot holes. The hot holes inject over the hole barrier of 4.6 eV at the anode [20] and cause the substrate
hole current through the oxide. Some holes are trapped in the oxide causing increase in the field at the cathode
[7]. This results in larger electron current injection from the cathode into the oxide by FN tunneling followed by
increased substrate current and hole trapping in the oxide. This positive feedback results in the oxide
breakdown. The time-to-breakdown is therefore proportional to exp (-B/E) with the slope constant B of about
505-509 MV/cm instead of 350 MV/cm reported earlier [28]. This 1/E model of the anode hole injection [28]
completely explains the oxide breakdown in thin oxide films of 5 to 10nm at high electric fields.
The knowledge of electron and hole effective masses and conduction and valence band offset values in
a metal-oxide-semiconductor (MOS) device can facilitate simulation of FN tunneling currents through a MOS
device at high fields. The FN onset field and the dielectric breakdown field can also be determined. The FN
onset field can be obtained for a minimum displacement current density of 10-8-10-9 A/cm2, and the dielectric
breakdown field can be obtained for a current density of 10 -4A/cm2, with the above knowledge. The thermal
SiO2 having an electron band offset of 3.2 eV and a carrier mass of 0.42m giving a slope constant of 254
MV/cm yields a breakdown field strength of about 9.5 MV/cm in the present study. Furthermore, the onset field
is the upper limit to which the oxide can work as a good insulator without injection and trapping of carriers in it.
The trapping of carriers causes degradation of the oxide and reduces its reliability.
IV.
Conclusion
The parabolic electron and hole effective masses in the thermal oxide are determined to be 0.42m and
0.58m for a free Fermi gas model of carriers at the emitting electrode. For this, a grounded Si n-channel
MOSFET and a MOSFET with -1 V substrate bias are utilized. These carrier masses are related to the band
offsets in SiO2/Si<100> MOS devices accurately though the MOSFET model. To an accuracy of one decimal
place, the SiO2/Si<100> conduction band and valence band offsets are calculated to be 3.2 eV and 4.6 eV
respectively. The SiO2 bandgap is calculated to be 8.9 eV. A MOSFET can be utilized to characterize MIS
structures with other insulating materials having negligible bulk traps or having bulk traps and exhibiting FN
conduction at high electric fields with the limitation that only 5 to 10nm thick insulator can be used. The
formulated oxide voltages utilizing experimental threshold voltages are considered more accurate for the
characterization. Also, the 1/E model of the anode hole injection over the hole barrier of 4.6 eV completely
explains the oxide breakdown in thin oxides of 5 to 10nm having a slope constant of about 505-509 MV/cm.
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